From the time-wise to space-wise GOCE observables

摘要

The observables of the GOCE three-axis gradiometerare taken in time, along the orbit and, in the timewiseproposal, filtered to stay in the measurement bandwidth,i.e. in the frequency interval between 0.005 and 0.1Hz. Asa consequence, the resulting “observable" is a convolutionof the original data stream with a time-wise weighting kernel.In other words, we cannot assume that the observationsare point-wise evaluations of any function and so, in a spacewiseapproach, any averaging or interpolating operation toobtain gridded spatial data has little sense.The problem is therefore to model correctly the observationalfunctionals, including the correlation along the orbit.This can be done by exploiting theWiener filter theory, usingthe prior knowledge of a geopotential model and the powerspectral density (PSD) of the measurement error.A numerical simulation from the EGM96 model (degreesbetween 50 and 300) is performed, showing that thealong track Wiener filter produces Trr spatialized observableswith an error standard deviation of the order of 5 mE.A covariance function of the estimation error is also providedby the Wiener filter theory. The use of these filteredobservables in a space-wise approach allows for the reconstructionof the gravity field in terms of spherical harmonicsup to degree 200.Key words. Satellite gradiometry, space-wise approach,measurement bandwidth, Wiener filter